Minimizing pleiotropic effects in modular and hierarchical system architectures

Complex systems are distinguished by high-pleiotropy interactions where the effect of a change in one physical element ripples throughout the system. Previous studies on this subject conclude that system pleiotropy, which measures such inter-dependencies across a system, varies inversely with the level of modularity adopted, suggesting maximum modularity is useful for minimizing the pleiotropic interactions in a system. Utilising the generalized NK modelling framework with a basic symmetrically distributed system model, in this paper, we demonstrate that there exists an optimal level of modularity as opposed to maximal modularity and an optimal level of hierarchy that minimizes the system pleiotropy in single-layered and hierarchically structured system architectures respectively. It is also identified that, proportional to system size, pleiotropy becomes sensitive to optimal levels of modularity and hierarchy. The assessment approach and analytical derivations presented in the paper provide a baseline for further research on restricting pleiotropic effects in practical systems.